A student was not sure how to solve an optimization problem, so he decided to use an AI tool. The question and the AI answer are listed below:

Question:

An investor is planning to allocate funds among three different investment options: Stocks, Bonds, and Real Estate. Each dollar invested in Stocks is expected to yield a return of $15\%,$ in Bonds $6\%,$ and in Real Estate $12\%.$ The investor has a total of $$100,000$ available for investment. Additionally, the investor wants to ensure diversification by allocating no more than $40\%$ of the total investment to any single option. Furthermore, the investor wants to ensure that the amount invested in stocks is not more than the amount invested in real estate. The goal is to maximize the total expected return from the investment portfolio. Formulate this problem as a Linear Programming $($LP$)$ model

AI Answer:

Let S$,$ B$,$ and R represent the amount of money $($in dollars$)$ invested in stocks, bonds, and real estate, respectively.

Maximize $0\mathrm{.}15$S $+0\mathrm{.}06$B $+0\mathrm{.}12$R

Subject to

S $+$ B $+$ R $<=100,000$

S $<=0\mathrm{.}40(100,000)$

B $<=0\mathrm{.}40(100,000)$

R $<=0\mathrm{.}40(100,000)$

S $<=$ R

S$,$ B$,$ R $>=0$

i$)$ Verify the formulation proposed by the AI tool: identify any mistakes and correct them. If you think there are no mistakes, then just write "the formulation is correct".

ii$)$ Model the verified formulation on Excel and use Excel solver to find the optimal investment allocation. Attach your Excel file, and please also add screenshot $.$

iii$)$ Based on your solution, how much should be invested in bonds?